Google Support provides step-by-step instructions for adding videos to your own custom playlists. On the desktop version of YouTube, open the video, click the Add To button underneath the player, and then select the check box next to the playlist you want to add the video to.
YouTube has replaced the default favorites list with the concept of generic playlists. As of December 2015, new YouTube accounts no longer have a favorites list, but instead have a Watch Later playlist by default.
LifeHacker also features a guide for adding videos to a playlist directly from YouTube video search results page.